From the Beginning to Plato

Glossary
Academy: Plato’s ‘school’, which he founded about 387 BC;
perhaps, at least in its original conception, mainly a
kind of research institute rather than a place of formal
teaching.
akrasia: (‘weakness of will’) a state of moral character,
excluded by Socrates but admitted by Plato, whereby
passions or pleasures either corrupt practical
judgement or cause action contrary to it.
anamnēsis: see ‘recollection’.
anthropomorphism: the practice of understanding the gods on the model
anthuphairesis,
antanairesis (‘alternate
subtraction’):
antilogic: see ‘dialectic’.
application (parabolē) of
areas:
of humankind, either in physical form or behaviour.
technique (now sometimes called the Euclidean
algorithm) used to find the greatest common measure
of two magnitudes (if they have one). Given two
magnitudes a 1 and a 2, one subtracts the lesser a 2 from
a 1 until one has a remainder a 3 less than a 2. If there is
no remainder, a 2 is the greatest common measure
of a 1 and a 2. If there is a remainder, one applies the
same technique to a 3 and a 2, and continues until a
common measure is found. It is not difficult to show
that if there is a common measure this technique will
find the greatest one. Twentieth-century scholars
have argued that anthuphairesis was the basis of a
pre-Euclidean theory of proportion, which they
usually associate with Theaetetus. See also
‘Commensurable’.
technique of constructing on a given straight line a
figure having a given area and satisfying other
conditions (e.g. being a square); one speaks of excess
(hyperbolē) or deficiency (elleipsis) if the
construction requires a straight line longer or shorter
than the given one. See also ‘geometrical algebra’.
aretē: virtue or excellence, a quality possession of which is
partly constitutive of the good life. Also used
collectively for the totality of such qualities.